Variational approach to the Coulomb problem on a cylinder

M. K. Kostov, Milton Walter Cole, G. D. Mahan

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e2/r. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a0/R, where a0 is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. EB is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, EB has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

Original languageEnglish (US)
Article number075407
Pages (from-to)754071-754075
Number of pages5
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume66
Issue number7
DOIs
StatePublished - Aug 15 2002

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curvature
Carbon Nanotubes
radii
Coulomb potential
Wave functions
Electron energy levels
Carbon nanotubes
divergence
perturbation theory
carbon nanotubes
wave functions
trends
energy

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Kostov, M. K. ; Cole, Milton Walter ; Mahan, G. D. / Variational approach to the Coulomb problem on a cylinder. In: Physical Review B - Condensed Matter and Materials Physics. 2002 ; Vol. 66, No. 7. pp. 754071-754075.
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Variational approach to the Coulomb problem on a cylinder. / Kostov, M. K.; Cole, Milton Walter; Mahan, G. D.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 66, No. 7, 075407, 15.08.2002, p. 754071-754075.

Research output: Contribution to journalArticle

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AB - We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e2/r. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a0/R, where a0 is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. EB is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, EB has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

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